A clear and self-contained introduction to discrete mathematics for undergraduates and early graduates. This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science, it is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). Being more narrowly focused than many discretemathematics textbooks and treating selected topics in an unusual depth and from several points of view, the book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gainfrom studying mathematics is the cultivation of clear and logicalthinking and habits useful for attacking new problems. More than 400 enclosedexercises with a wide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. The readers will appreciate the lively and informal style of the text accompanied by more than 200 drawingsand diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, andeven experts in combinatorics may occasionally learn from pointers to research literature or from presentations of recent results. Invitation to Discrete Mathematics should make a delightful reading both for beginners and for mathematical professionals.The main topics include: elementary counting problems, asymptotic estimates, partially ordered sets, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, Ramsey's theorem, and combinatorial applications of linear algebra.General mathematical notions going beyond the high-school level are thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some ofthe more advanced sections of the book. INDICE: Preface to the second edition Preface to the first edition Introduction and basic concepts Orderings Combinatorial counting Graphs: an introduction Trees Drawing graphs in the plane Double-counting The number of spanning trees Finite projective planes Probability and probabilistic proofs Order from disorder: Ramsey's theorem Generating functions Applications of linear algebraAppendix Bibliography Hints to selected exercises Index
- ISBN: 978-0-19-857043-1
- Editorial: Oxford University
- Encuadernacion: Cartoné
- Páginas: 464
- Fecha Publicación: 09/10/2008
- Nº Volúmenes: 1
- Idioma: Inglés